Optics Communications 266 (2006) 604–608 www.elsevier.com/locate/optcom

Experimental constraints of using slow- in sodium vapor for light-drag enhanced relative rotation sensing

Renu Tripathi *, G.S. Pati, M. Messall, K. Salit, M.S. Shahriar

Department of Electrical and Computer Engineering, Northwestern University, Evanston, IL 60208, United States

Received 30 December 2005; received in revised form 23 May 2006; accepted 23 May 2006

Abstract

We report on experimental observation of electromagnetically induced transparency and slow-light (vg c/607) in atomic sodium vapor, as a potential medium for a recently proposed experiment on slow-light enhanced relative rotation sensing [Shahriar, et al. Phys. Rev. Lett. (submitted for publication), http://arxiv.org/abs/quant-ph/0505192.]. We have performed an interferometric measurement of the index variation associated with a two- resonance to estimate the characteristics of the medium that are relevant to the slow-light based rotation sensing scheme. We also show that the presence of counter-propagating pump beams in an optical Sagnac loop produces a backward optical phase conjugation beam that can generate spurious signals, which may complicate the measurement of small rotations in the slow-light enhanced gyroscope. We identify techniques for overcoming this constraint. Conclusions reached from the results presented here will pave the way for designing and carrying out an experiment that will demonstrate the slow-light induced enhancement of rotation sensing. 2006 Elsevier B.V. All rights reserved.

PACS: 45.40.Cc; 42.50.p; 42.50.Nn; 82.70.y; 39.20.+q; 39.90.+d

Keywords: Rotation sensing; Optical gyroscope; Slow-light; Electromagnetically induced transparency; Sodium vapor; Mach–Zehnder interferometer

Extreme dispersion induced by electromagnetically sensing. In this case, the rotational fringe shift is aug- induced transparency (EIT) can reduce the speed or group mented by the group index or the dispersion in the med- velocity of light by many orders of magnitude compared to ium, which, for realistic conditions, can yield many the in [1–4]. Recently, there has been orders of magnitude improvement in the sensitivity of the a significant interest in the physics and applications of gyroscope [11]. slow-light. Typical applications include schemes where a An experimental implementation of the interferometric controllably varied is used to realize optical gyroscope relies on using an EIT medium, so that the coun- delay lines, buffers, etc. [5,6], as well as techniques where ter-rotating optical fields experience resonant dispersion reversible mapping of photon pulses in atomic medium along the entire optical path. A relative motion between are used for quantum state storage [7–9]. Recent proposals the medium and interferometer is also needed [11]. This have also envisioned using slow-light to enhance the rota- gives rise to a rotational fringe shift that depends on the tional sensitivity of an interferometric optical gyroscope magnitude of the dispersion in the medium. We have con- [10,11]. Such an interferometer may use slow-light induced sidered Na atoms in a dilute vapor as an example of an dispersive drag for enhanced sensitivity in relative rotation experimental medium for this purpose. We have studied EIT in Doppler-broadened optical transitions of the D1 line in Na vapor, and experimentally measured its disper- * Corresponding author. Tel.: +1 812 841 3529; fax: +1 847 491 4455. sion characteristics that are relevant to its use in a E-mail address: [email protected] (R. Tripathi). slow-light enhanced Sagnac interferometer. In particular,

0030-4018/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2006.05.061 R. Tripathi et al. / Optics Communications 266 (2006) 604–608 605 magnitudes of the index change and the dispersion, under a Fig. 1 shows energy levels selected for a three-level K- narrow EIT resonance, have been measured by a phase type system in the D1 line of Na. A frequency-tuned cw delay obtained using a homodyne detection scheme. Precise dye laser with a narrow linewidth (<1 MHz) is used to measurements of these values help us infer the dynamic derive the optical beams. The pump beam is locked to 2 2 0 range as well as the magnitude of the sensitivity enhance- the 3 S1/2, F = 1 and 3 P1/2, F = 1 transition using satu- ment [11]. An excellent agreement is obtained while com- rated absorption. The probe laser is derived by frequency paring the magnitudes of the first-order dispersion shifting the pump beam with an acousto-optic modulator estimated from the time delay of slowed optical pulses (AOM). The frequency difference between the pump and and the slope of the dispersion curve obtained from the probe laser field is set equal to the frequency-splitting 2 interferometric measurements discussed above. While the (1.772 MHz) between the ground-states 3 S1/2, F = 1 and 2 results on slow-light in hot Na vapor have significant rele- 3 S1/2, F =2. vance to other potential applications, such as for optical The experimental arrangement is shown in Fig. 2. The data buffering or quantum memory, we have chosen here pump and the probe beams are cross-linearly polarized. to focus only on the issues that are most relevant to the They propagate collinearly in a 10 cm long sodium vapor application of this process to the enhancement of rotation cell. The beams are focused inside the cell to a beam waist sensing. (1/e in intensity) of 100 lm that corresponds to a confo- cal distance of 5 cm. The orthogonality of the pump and the probe polarizations allows us to filter the pump at the output in order to measure the absorption and dispersion 2 2 F’=1 3 P1/2 Δ 3 properties of the probe field very accurately. As the laser δ excitation in alkali atoms like sodium involves many hyper- fine Zeeman sublevels, the K-type scheme often departs from an ideal EIT system in the presence of a stray mag- ω netic field. The cell is, therefore, magnetically shielded ω 2 589.8 nm 1 using two-layers of l-metal to minimize the effects of stray Pump Probe magnetic fields. During the experiment, the sodium cell is heated to a steady temperature of 100 C using bifilarly 2 wound coils that produce a negligible magnetic field. 2 F=2 As shown in Fig. 2, the frequency of the probe is contin- 3 S1/2 1.772 GHz 1 uously scanned around the two-photon resonance condi- F=1 tion, using a double-pass acousto-optic frequency shifter

Fig. 1. Energy level structures in D1 line of sodium used as a three-level to observe the linewidth of EIT. The pump intensity is K-system. set to nearly 20 W/cm2, which corresponds to a Rabi

PZT Mirror NDF Interferometer

HWP

BS PBS PBS Det PC Det

Arb. Pulse Probe Pol Gen. HWP Lens Lens Magnetically Back-prop. shielded Na pupump vapor cell BS NDF AOM 2 Freq. Mixer AOM 1 f = 80 MHz f =1.661 GHz Pump

PBS

HWP

Dye Laser Ar+ Laser

Fig. 2. Experimental setup used to observe EIT, slow-light and PC in Na vapor. HWP = half-wave plate; PBS = polarizing beam splitter; NDF = neutral density filter; AOM = acousto-optic modulator; Pol = polarizer; and Det = detector. 606 R. Tripathi et al. / Optics Communications 266 (2006) 604–608 frequency X 40 GHz. The ratio of the pump to probe 0.1 EIT resonance intensities is set to 10. The EIT linewidth is found to be Δn 0.08 linear dispersion regime -13 -1 1 MHz. This is limited by the transit time (1 ls) of ) dn/dω ~ 1.89 x 10 Hz the atoms and can be improved upon by adding a buffer -8 0.06 gas in the vapor cell. A maximum probe transmission of 0.04 n (x 10

23% has been observed. Fig. 3a shows a sequence of EIT Δ 0.02 resonances with increasing pump intensity. A frequency- 0 dithered lock-in-detection is used to observe the EIT signal in the presence of the residual-pump beam. Fig. 3b shows -0.02 the corresponding change in the slope of the lock-in-detec- -0.04 tion signal with increasing in pump intensity. -0.06

The dispersion characteristic associated with sub-natu- Magnitude (a.u.) & -0.08 ral EIT line-widths is measured using a homodyne method [13] based on a Mach–Zehnder interferometric configura- -0.1 tion, as shown in Fig. 2. An unperturbed fraction of the -5 -4 -3 -2 -1 0 1 2 3 4 5 δ (ω -ω ) (MHz) probe beam traversing an equivalent optical path outside 2 1 the cell is used as a reference beam in the homodyne detec- Fig. 4. Interferometrically measured variation associated tion scheme. The reference beam and the transmitted EIT with EIT dispersion. signal are interferometrically combined at the output. The signal intensity detected on the photodiode is propor- tional to the phase shift D/ =(2p/k)[n(x) 1]L, intro- Fig. 4 shows the index variation as a function of the differ- duced by the dispersion of the atomic medium, and is ence frequency d. Several measurements were taken to given by iD / 2jEpjjErefjcos[D/ + /ref], where Ep and Eref measure the slope of the positive dispersion profile at the are the amplitudes of the probe and the reference, respec- center of the EIT resonance i.e., (on/ox)jd =0 (1.89 · 13 1 tively, L is the active interaction length, and /ref is the 10 rad s) that corresponds to a slow group velocity phase of the reference beam. A piezo-mounted mirror is vg (c/607) in the medium. This also corresponds to a used to adjust the reference phase to p/2 such that the refractive index variation Dn 1.89 · 107 over a probe observed magnitude of the photo-current is directly pro- frequency bandwidth Df = 1 MHz. The accuracy of these portional to Dn(x)[=n(x) 1] for jkDn(x)Lj1, valid measurements is subsequently verified by pulse delay mea- if jDnj106 (typical for a dilute atomic medium). The surements from a slow-light experiment. Similarly, the 2 2 frequency of the probe laser is swept at a faster rate magnitude of the second-order dispersion (o n/ox )jd =0 (1 KHz) so that only a negligible drift occurs between the has also been estimated from a polynomial fit to the disper- interferometer arms while measuring the phase delay D/. sion profile, over a frequency range Df = 1 MHz. This

0.25 I ~ 20 W/cm2 0.2 p 2.I p 0.15 3.I p 0.1

0.05 Probe transmission 0 -5 -4 -3 -2 -1 0 1 2 3 4 5 δ ω ω = ( 2- 1) (MHz)

--- Lock-in-detection signal 0.1

0

-0.1 Magnitude (a.u.)

-5 -4 -3 -2 -1 0 1 2 3 4 5 δ ω ω =( 2- 1) (MHz)

Fig. 3. Variation of EIT line width with pump intensity: (a) detector output; and (b) lock-in-detection signal. R. Tripathi et al. / Optics Communications 266 (2006) 604–608 607

15 2 2 value being small (2.24 · 10 rad s ) corresponds to ref. pulse negligible pulse spreading during slow pulse propagation 0.07 pr = 0 in the EIT medium. Our results suggest that the present 347 KHz 0.06 522 KHz atomic medium can be employed in an interferometric 1.317 MHz 1.709 MHz gyroscope to demonstrate drag induced sensitivity enhance- 0.05 ment nearly by a factor of 600 (equal to group index ng). For improved performance, the slope of the linear disper- 0.04 sion can be increased using a medium with larger transit 0.03 times by adding a buffer gas into the cell. Magnitude (V) In order to observe the slowing of probe pulses due to 0.02 the steep normal dispersion in the EIT medium, short probe pulses (FWHM 400 ns) with an arbitrary delay 0.01 and smooth profile (nearly transform limited) are gener- 0 ated using an RF mixer and a digital pulse generator with a frequency filter. During the experiment, the pump beam -6 -4 -2 0 2 4 6 8 Time (sec) -7 remains on continuously. The group velocity, vg, of the x 10 probe pulse, is estimated accurately by measuring the time Fig. 6. Pulse spreading due to second-order dispersion observed by delay with respect to a reference probe pulse propagating frequency detuning the probe carrier frequency away from two-photon outside the cell. This is then used to measure indirectly resonance. the linear dispersion coefficient (on/ox)jd =0 at the center of the EIT resonance, and is compared with the comple- case, the pulse undergoes asymmetric spreading as it expe- mentary interferometric measurements. riences dispersion which is no longer linear over one half of Fig. 5 shows the slowed probe pulses with respect to a its bandwidth. Also, as the frequency is detuned away from reference pulse and the corresponding time delays. The resonance, the transmission of the probe pulse decreases presence of residual magnetic fields due to the heating coils and smaller time delays are observed with respect to the provide additional mechanisms for dephasing and thus reference pulse, as expected. broaden the EIT linewidth and reduce the dispersion To realize the feasibility of light-drag induced rotational induced time delay. A maximum time delay of 202 ns sensitivity enhancement near an atomic resonance, we have has been observed by temporarily switching off the current considered a common path Sagnac interferometer where to the coils. The value of vg corresponding to this time the atomic medium, besides the forward-propagating pump delay is found to be c/607, which agrees very well with and probe, also encounters a back-propagating pump our previous measurement. As can be also seen in Fig. 5, resulting from the common path beam, as shown in negligible pulse spreading is observed over the input pulse Fig. 7. This geometry, while crucial in canceling the effect bandwidth. This also confirms the fact that the dispersion of external vibrations for example, can form a four-wave is linear over the pulse bandwidth. Fig. 6 shows significant mixing (FWM) process and write nonlinear gratings via pulse spreading when the carrier frequency of the probe is EIT to generate a backward optical phase conjugate (PC) detuned above the two-photon resonance condition. In this beam. In order to test this effect, we used a back-propagat- ing pump which is frequency degenerate and has the same polarization as the forward pump [12]. The process can be 0.07 Ref. pulse understood in terms of a two-photon induced grating delay (τ) = 165 ns, v ~ c/496 g formed in the ground-state coherence q X0X = X02 202 ns, vg ~ c/607, (Curr. off) 12 / b ð þ 0.06 2 1=2 XbÞ expfi½ðx2 x1Þt ðk2 kbÞzg by the probe and backward pump, when the atoms are optically pumped 0.05 0 into the dark superposition state. Here Xb, X are the Rabi frequencies, kb, k2 are propagation vectors and x1, x2 are 0.04 optical frequencies associated with the backward pump 0.03 and probe, respectively. The forward pump produces a Magnitude (V) phase matched read-out of the grating to generate a back- 0.02 ward PC beam at the probe frequency. It is observed exper- imentally that even though the forward pump atomic 0.01 transition is Doppler-broadened, only a low intensity backward pump is needed to produce the PC beam. 0 Fig. 8 shows the measured phase conjugate reflectivity at -8 -6 -4 -2 0 2 4 6 8 10 -7 the beam splitter output (Fig. 2) as a function of the probe Time (sec) x 10 detuning. The frequency width (FWHM 1 MHz) is Fig. 5. Probe pulse slowing using EIT induced dispersion in sodium nearly equal to the EIT linewidth and the measured PC vapor. reflectivity is 0.017. Such a signal can circulate in an 608 R. Tripathi et al. / Optics Communications 266 (2006) 604–608

DeDet

Active slow-light medium

Fig. 7. A common path Sagnac interferometer containing a slow-light medium for light-drag enhanced rotation sensing.

0.02 as a possible candidate for a light-drag enhanced relative rotation sensor. We have determined that an enhanced fac- 0.018 tor of 600 is readily achievable. Such a medium is cur- 0.016 rently being used in an optical Sagnac interferometer to 0.014 observe sensitivity enhancement. We have also shown that

0.012 the presence of an unavoidable back-propagating pump in a common path interferometer produces optical phase con- 0.01 jugation at low optical power, which is detrimental to 0.008 fringe shift measurement, and have suggested schemes that 0.006 can help circumvent this problem.

Phase conjugate reflectivity 0.004 Acknowledgement 0.002 0 This work was supported in part by the AFOSR and the -8 -6 -4 -2 0 2 4 6 8 ARO MURI program. =( 2- 1) (MHz)

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